Development of adjoint method of characteristics code for fast reactor

In order to obtain reference with the consideration of the heterogeneous geometry for the fast reactor core calculation, a new MOC (Method of Characteristics) code which can calculate both forward and adjoint fluxes has been developed in this study. For the safety analysis of the fast reactor core, we need many data, such as reactivity coefficient, effective neutron ratio, sensitivity coefficient etc. To evaluate these data, perturbation calculation is useful. To evaluate the imperceptible variation accurately by perturbation calculation, the evaluation of adjoint flux as well as forward flux is necessary in the same system. Integro-differential transport equation of the forward flux can be written as equation (1), and that of adjoint flux can be written as equation (2). Equation (3), which is generally used for MOC, can be obtained from equation (1). In this study, equation (4) is obtained from equation (2)in the same way. By the implementation of equation (4)to the existing MOC code, the adjoint flux can be obtained in MOC calculation. dΦg (r + sΩl,Ωl) / ds + Σtg (r + sΩl)Φg (r + sΩl,Ωl) = qg (r + sΩl) (1); dΦ*g (r - sΩl,Ωl) / ds + Σtg (r - sΩl) Φ*g (r - sΩl,Ωl) = q*g (r - sΩl) (2); Φg (r + tΩl,Ωl) = exp[-τg (r,r + tΩl)] x (Φg (r,Ωl) + ∫0t ds qg (r + sΩl) exp[τg (r,r + sΩl)]) (3); Φg (r - tΩl,Ωl) = exp[-τg (r - tΩl, r)] x (Φ*g (r,Ωl) + ∫0t dsqg (r - sΩl) exp[τg (r - sΩl, r)]) (4) In order to validate the above method, calculation was performed for the cell of fast reactor with 7 group cross section. MOC calculation conditions are the same between forward calculation and adjoint flux calculation (track spacing is between 0.010 and 0.009 cm, azimuthal angle division is 64 per 360 degrees, polar angle division is 3 per 90 degrees). The results are shown in table 1. The eigenvalue of adjoint flux calculation was compared with that of forward flux calculation. The difference between the two is 1.4E-6. The CPU time is almost the same. This result shows the validity of the above method. The result of whole core calculation of fast reactor will be described in the full paper